The statistics of the ordering of chiral ribbons on a honeycomb lattice
The statistics of the ordering of chiral ribbons on a honeycomb lattice
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DOI：
10.1088/1742-5468/ac1263
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发表时间：
2021-05
期刊：
影响因子：
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通讯作者：
Maxine M. McCarthy;William S. Fall;X. Zeng;G. Ungar;G. Gehring
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文献类型：
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作者：
Maxine M. McCarthy;William S. Fall;X. Zeng;G. Ungar;G. Gehring
提出并研究了一个描述复杂液体和液晶中自发手性同步的新模型。具有左旋或右旋180 °扭转的带状分子柱的片段位于蜂窝晶格的键上，使得三个带状物在六边形蜂窝的顶点处相遇。如果三个带具有相同的手征性，则每个顶点的能量是最小的，否则是+<$，并且基态是纯手征的，即所有带具有相同的手性。在此顶点模型中，由单个带连接的两个顶点的能级为− 2、0和+2。Monte Carlo模拟表明，该模型是相同的伊辛自旋模型上的Kagome晶格，其中网站的能量结构是完全不同的。顶点和伊辛自旋模型的排序的等价性也显示解析。无序和基态之间的能量差，4J的自旋模型中，是有关的过渡温度为Kagome晶格使用的确切结果，T c = 2.14 J。一个单一的网站的有序能量差是50%以上的顶点模型。由于重复计算，顶点模型的热力学能量被校正了1/3，这使得顶点模型的比热也与自旋模型的比热相等。其他类似的模型，有一个不寻常的网站和热力学能量之间的关系进行了简要讨论。
A novel model, devised to describe spontaneous chirality synchronization in complex liquids and liquid crystals, is proposed and studied. Segments of ribbon-like molecular columns with left- or right-handed 180° twist lie on the bonds of a honeycomb lattice so that three ribbons meet in a vertex of the hexagonal honeycomb. The energy of each vertex is a minimum if the three ribbons have the same chirality, −ɛ, and is +ɛ otherwise, and the ground state is homochiral, i.e. all ribbons have the same handedness. The energy levels for two vertices linked by a single ribbon are either −2ɛ, 0 and +2ɛ in this vertex model. Monte Carlo simulations demonstrate that this model is identical to an Ising spin model on a Kagome lattice, for which the site energy structure is quite different. The equivalence of the ordering of the vertex and Ising spin models is also shown analytically. The energy difference between the disordered and ground states, 4J in the spin model, is related to the transition temperature for the Kagome lattice using the exact result, T c = 2.14 J. The ordering energy difference for a single site is 50% higher for the vertex model. The thermodynamic energy for the vertex model is corrected by a factor of 1/3 due to double counting and this makes the specific heat of the vertex model also equal to that of the spin model as expected. Other similar models where there is an unusual relation between the site and thermodynamic energies are discussed briefly.